The man who killed a New Plymouth jogger could serve a longer prison sentence if a Crown appeal is successful.

Matthew Kinghorn pleaded guilty in October last year to murdering Anne Elizabeth McCullough, 45. He was sentenced to a minimum non-parole period of 13 years in jail.

McCullough, a mother of two, died of multiple injuries after Kinghorn deliberately ran her down in his car on October 20, 2012, as she jogged along a country road on the outskirts of New Plymouth.

Crown lawyer Madeleine Laracy argued yesterday in the Court of Appeal in Wellington that Justice Rodney Hansen had made legal errors during sentencing, the New Zealand Herald reported.

The Crown had argued Kinghorn had killed McCullough during a sexual attack, which would mean he would serve the maximum non-parole life sentence of 17 to 25 years.

But Justice Hansen found there was not enough evidence and gave Kinghorn 15 years as the minimum sentence of imprisonment. He deducted two years because Kinghorn had pleaded guilty and appeared to show remorse.

The Herald reported Laracy saying yesterday that Justice Hansen had made comments during sentencing agreeing with the Crown's position.

McCullough's death was therefore a "reckless killing" resulting from the attack and Kinghorn's offending had been carried out with extreme callousness and depravity.

Kinghorn's lawyer, Julian Hannam, said Hansen's sentencing decision was correct and provided evidence showing the attack on McCullough had not been sexually motivated.

The Crown's argument that Kinghorn's crime was exceptionally brutal, callous and depraved was their "least powerful" argument and he expected it would be dismissed, he said.

Hannam said it was unusual for the Crown to appeal a sentence.

"It's to make sure the family gets a good hearing, so they know everything that can be done has been done. My client understands that."